How can I blend / flllet two objects of different shape?
Increase vertex density and Loop Tools Circle, Bridge



Various Stages of Editing.


Cube in Edit mode, Loop Cut on twice in X and Y Planes.  Delete Middle Squares of vertices
Think about vertex count of target Cylinder
Select Perimeter of hole and Loop Tools Circle in Tool Panel
Extrude in Z Axis
Loop Cut and Shape with Proportional Edit 
The result is compatible with another Cylinder with same vertex count.
The Cylinder is not shown above, [Join] two separate objects if necessary
Use Bridge Tool to connect to perimeter of Cylinder
Bridge examples can be found by searching here at BSE